﻿The 
  Decay 
  of 
  Waves 
  in 
  a 
  Canal. 
  483 
  

  

  (9) 
  The 
  •• 
  electric 
  absorption 
  " 
  o£ 
  gas 
  is 
  found 
  to 
  be 
  closely 
  

   connected 
  wirh 
  the 
  size 
  o£ 
  the 
  cathode 
  fall, 
  which 
  leads 
  to 
  

   the 
  assumption 
  that 
  the 
  absorption 
  is 
  chiefly 
  caused 
  by 
  

   positive 
  ions 
  being 
  shot 
  into 
  the 
  cathode. 
  

  

  In 
  conclusion, 
  I 
  wish 
  to 
  thank 
  Sir 
  J. 
  J. 
  Thomson 
  for 
  

   suggesting 
  the 
  work 
  to 
  me. 
  

  

  I 
  have 
  also 
  much 
  pleastire 
  in 
  thanking 
  Mr. 
  E. 
  Everett 
  for 
  

   his 
  assistance 
  with 
  some 
  of 
  the 
  o-lasswork. 
  

  

  Careudisii 
  Laboratory, 
  

   May 
  1st, 
  1900. 
  

  

  LT. 
  The 
  Decay 
  of 
  Waves 
  in 
  a 
  Canal. 
  By^ 
  . 
  J. 
  Harrison, 
  

   B.A.^ 
  Fellow 
  of 
  Clare 
  College^ 
  Isaac 
  Keivton 
  Student 
  in 
  the 
  

   University 
  of 
  Cambridge 
  *. 
  

  

  §1. 
  TX 
  a 
  paper 
  published 
  recently 
  Dr. 
  R. 
  A. 
  Houstoungave 
  

   X 
  the 
  results 
  of 
  some 
  experiments 
  on 
  the 
  damping 
  of 
  

   long 
  waves 
  in 
  a 
  rectangular 
  trough 
  t 
  • 
  The 
  observed 
  damping 
  

   is 
  from 
  two 
  to 
  three 
  times 
  as 
  great 
  as 
  that 
  calculated 
  from 
  

   the 
  formula 
  obtained 
  by 
  him. 
  In 
  this 
  paper 
  an 
  explanation 
  of 
  

   the 
  discrepancy 
  is 
  attempted. 
  It 
  has 
  been 
  shown 
  by 
  the 
  

   present 
  author 
  that 
  under 
  certain 
  circumstances 
  the 
  air 
  exerts 
  

   a 
  great 
  damping 
  influence 
  on 
  water 
  waves!. 
  It 
  may 
  be 
  as 
  

   well 
  to 
  emphasize 
  here 
  the 
  cause 
  of 
  this 
  influence, 
  as 
  it 
  might 
  

   appear 
  strange 
  that 
  a 
  fluid 
  of 
  such 
  slight 
  density 
  as 
  air 
  coald 
  

   afliect 
  the 
  decay 
  of 
  water 
  waves. 
  The 
  modulus 
  of 
  decay 
  r 
  of 
  

   wave-motion 
  at 
  the 
  surface 
  of 
  a 
  single 
  fluid 
  of 
  depth 
  large 
  

   compared 
  with 
  the 
  wave-length 
  \ 
  of 
  the 
  motion 
  depends 
  on 
  

  

  \- 
  : 
  when 
  there 
  is 
  another 
  fluid 
  superposed 
  r 
  depends 
  on 
  V 
  ; 
  

   and 
  thus 
  when 
  \ 
  is 
  large 
  the 
  difference 
  is 
  considerable, 
  

   despite 
  the 
  small 
  density 
  of 
  air. 
  Now 
  the 
  waves 
  considered 
  

   by 
  Dr. 
  Houstoun 
  in 
  his 
  paper 
  are 
  of 
  long 
  wave-leu 
  gth, 
  and 
  

   it 
  was 
  supposed 
  that 
  the 
  air 
  might 
  have 
  some 
  considerable 
  

   effect. 
  But 
  it 
  might 
  have 
  been 
  surmised 
  a 
  priori 
  that 
  this 
  

   would 
  not 
  be 
  the 
  case, 
  as 
  the 
  effect 
  of 
  the 
  finite 
  depth 
  is 
  

  

  itself 
  to 
  produce 
  a 
  first 
  approximation 
  of 
  the 
  order 
  V. 
  On 
  

   obtaining 
  the 
  analytical 
  expression 
  for 
  the 
  damping 
  due 
  to 
  

   the 
  air, 
  there 
  was 
  found 
  to 
  be 
  not 
  the 
  slightest 
  ground 
  for 
  

   supposing 
  that 
  we 
  have 
  here 
  the 
  explanation 
  of 
  the 
  discrepancy. 
  

   Although 
  a 
  consideration 
  of 
  the 
  influence 
  of 
  the 
  air 
  is 
  of 
  no 
  

   use 
  in 
  our 
  present 
  investigation, 
  the 
  expressions 
  for 
  the 
  

  

  * 
  Communicated 
  bv 
  the 
  Author. 
  

  

  t 
  Phil. 
  Map-. 
  ;6", 
  vol. 
  xyii. 
  pp. 
  154-164. 
  

  

  + 
  Proe. 
  Lend: 
  Math. 
  Sec. 
  ser. 
  2, 
  vol. 
  yi. 
  p. 
  396. 
  

  

  